UNIQUENESS OF AN OPTIMAL CONTROL OF NONLINEAR INFINITE SPACE OF NEUTRAL FUNCTIONAL DIFFERENTIAL SYSTEMS WITH DISTRIBUTED DELAYS IN THE CONTROL.
Publication Date : 01/03/2018
Abstract In this paper, Nonlinear Infinitely Space of Neutral Functional Differential Systems with Distributed Delays in the Control of the form: d/dt [D(t,x_t )]=L(t,x_t ) x_t+∫_(-∞)^o▒A (t)x(t+θ) +∫_(-h)^O▒[ d_θ H(t,θ)]u(t+θ)+f(t,x_t ) was presented for study. To obtain the solution of the system, we first of all linearize the nonlinear system for the work to be less tedious using Chukwu (1992)-like arguments. After linearization, we integrated the linearized system and obtained the mild solution of the system from which we extracted the set functions (reachable set, target set, attainable set) upon which our study hinged. Use was made of the Unsymmetric Fubuni Theorem to establish the results. It was established that the optimal control is unique. The establishment of the uniqueness of optimal control provided a new approach for the proof of the existence of an optimal control.
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